The evolution of the antiferromagnetic order parameter in CeFeAsO1−xFx as a function of the fluorine content x was investigated primarily via zero-field muon-spin spectroscopy. The long-range magnetic order observed in the undoped compound gradually turns into a short-range order at x=0.04, seemingly accompanied or induced by a drastic reduction of the magnetic moment of the iron ions. Superconductivity appears upon a further increase in doping (x>0.04) when, unlike in the cuprates, the Fe magnetic moments become even weaker. The resulting phase diagram evidences the presence of a crossover region, where the superconducting and the magnetic order parameters coexist on a nanoscopic range.